The Riverhead School Board of Education is leaning toward filling two open seats, left vacant following the abrupt resignations of Amelia Lantz and Ann Cotten-DeGrasse last month, with candidates they hope to appoint after an interview process.

As an increasing number of students continue to enroll in the Riverhead school district more quickly than administrators ever anticipated, school board member Greg Meyer wants to renew talks between the district and the town about building a new school at the Enterprise Park at Calverton.

Riverhead School District Superintendent Nancy Carney is expected to give a presentation about Common Core practices within English Language Arts and math in grades kindergarten through second grade, according to Tuesday night’s school board meeting agenda.

For the first time this past April, the state’s ELA and math assessments included elements of what’s known as the Common Core State Standards Initiative. The Common Core is a new set of national standards designed to raise the bar for classroom instruction and help “prepare students for college and careers in the 21st century,” state officials say. The initiative primarily requires instructors to teach more non-fiction and more rigorous math to students at a younger age.

In addition to Common Core, the school board is expected to discuss its budget-planning timeline for the 2014-15 school year.

On Jan. 14, the school board will go over its tentative budget goals and will hold a special meeting Jan. 21 to discuss personnel issues in executive session.

Ms. Carney is then expected to hold the following budget presentations:

Feb. 11: General support, benefits and debt service

Feb. 25: Regular day school budget, transportation and facilities

March 11: Special education, PPS, guidance and other instructional items

March 25: Revenue and tax levy

April 8: Tentative budget

The school board is expected to adopt the 2014-15 spending plan by April 22 and release it to the public by May 2.

The final budget hearing is set for May 13 — one week before the vote.

As for the school board race, president Ann Cotten-DeGrasse, vice president Greg Meyer and member Kimberly Ligon are up for reelection. Board of Education candidate petitions are due April 21.